Euler Number

An introduction and definition of the Euler Number in fluid mechanics

The Euler Number is a dimensionless value common used for analyzing fluid flow dynamics problems where the pressure difference between two point is an important variable. The Euler Number can be interpreted as a measure of the ratio of pressure forces to inertial forces.

The Euler Number can be expressed as

Eu = p / (ρ v²) (1)

where

Eu = Euler number

p = pressure (Pa)

ρ = density (kg/m³)

v = fluid flow velocity (m/s)

The pressure difference as shown below is often used

Eu = dp / (ρ v²) (2)

where

dp = differential pressure (Pa)

The combination below is called the pressure coefficient

pressure coefficient = dp / (1/2 ρ v²) (3)

A special version of the Euler Number is in general referred to as the Cavitation Number.

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